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“The trouble with facts is that there are so many of them.”—Samuel McChord Crothers

Cosmetic formulation aspires to be a true science, but compared to physics or chemistry, it has very little in the way of theoretical frameworks to guide this work. Most formulation is based on empirical knowledge or trial-and-error experimentation. There is no equivalent of F=ma or E=mc2 for making a shampoo or microemulsion.

One of the few general tools available is hydrophil/lipophil balance (HLB) theory, but it is restricted to nonionic emulsions and, even within that narrow realm, still has shortcomings. Beyond HLB, there is a vast theoretical desert where phase diagrams provide a welcome oasis, offering a systematic approach to analyzing complex systems. Personal care products are complex—let there be no doubt. The sheer number of variables and the abundance of radically different product formats underlie the unique challenge faced at the lab bench.

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Phase diagrams often are seen at meetings and in literature, but it is easy to skim over them without appreciating their value. Phase diagrams allow exploration of the properties of single materials, mixtures and assemblies. They help in analyzing systems as diverse as aerosol gas blends, deodorant sticks and fragranced lotions. When analytical methods are applied to the separate phases, a clear picture emerges of the complex interactions resulting from multiple variables.

The Shape of Things

A simple case is the behavior of water. As the temperature changes under standard atmospheric conditions, water changes from a solid to a liquid to a gas (Figure 1a). When the pressure varies, the situation immediately gets more complicated (Figure 1b). New possibilities arise: to go directly from solid to gas in a process called sublimation and the triple point—where solid, liquid and gas coexist.

Charles Cagniard de la Tour (1777–1859) is responsible for the deeper understanding of water. In 1822, he discovered the critical point in his famous cannon barrel experiments. He listened to discontinuities in the sound of a rolling flint ball in a sealed cannon filled with fluids at various temperatures. Above a certain temperature, the densities of the liquid and gas phases become equal, resulting in a single supercritical fluid phase. While investigating the effect of heat and pressure on liquids, Cagniard de la Tour found that there was a certain temperature for each phase above which liquids refused to remain liquid, passing into the gaseous state—no matter the amount of pressure to which they were subjected.

The square shape of Figure 1b is appropriate for two variables. For three variables (such as water, oil and surfactant), a triangle is needed. Point A is 100% oil, Point E is 100% surfactant and Point G is 100% water. There is no water along line AE, so every point along the line is a different blend of oil and surfactant. As water is added drop by drop, information along the lines AG, BG, CG, DG, EG is created that completes a picture of the system.

Friberg(1) used phase diagrams in a classic paper on emulsion science. He showed that since macroemulsions are thermodynamically unstable, the known stability could only be accounted for by the presence of liquid crystal phases in the external phase. Summarizing the power of this approach, Friberg wrote: “This hypothetical case shows how many hitherto unexplained properties of emulsions can find a reasonable explanation when ternary systems prepared under equilibrium conditions are used.”

Graham Barker(2) used phase diagrams to explain the organization of sodium stearate molecules when placed in mixtures of water and organic solvent. Sodium stearate often is used to create deodorant sticks, with specific structures needed for structural integrity. Barker’s phase diagram is a mini-course in the possible aggregate structures of amphiphilic molecules.

The sodium stearate, with a polar end and nonpolar tail, assembles based on the environment. In a predominantly polar solvent blend, the polar heads will be on the outside, either in the form of a spherical micelle, a rod or a lamellar sheet. With a nonpolar solution, the tails will stick out. The diagram shows this occurs when the dodecanol exceeds 50%.

Determining the structures requires tests, such as X-ray diffraction or birefringence, which appears in materials that are anisotropic, meaning directionally dependent. It can be observed in a polarizing microscope—between the crossed polarizers, a birefringent sample will appear bright against a dark (isotropic) background. X-ray diffraction can quantify the distance between layers in a lamellar region.

In its company literature(3), Gattefossé showed how microemulsions can be formulated in a systematic way, using titrations and visual inspection to create a relevant phase diagram. Microemulsions are complicated systems, needing water, oil, a surfactant and cosurfactant to achieve the desired results. This requires four components, but a triangle has three sides. The system is properly a three dimensional pyramidal structure. To make a manageable experiment, the surfactant/cosurfactant ratio is fixed, which has the effect of taking a slice out of the pyramid, thus returning to a triangle—called a pseudoternary diagram.

The surfactant/cosurfactant blend is added to the oil, as water is slowly titrated in with mixing. Some areas will be hazy, but the microemulsion areas will be clear. As the test is repeated with different surfactant blends, different patterns will result. This is a wonderful example of the power of phase diagrams to systematize formulation work.

In the 1990s, Friberg and his colleagues produced a number of papers focusing on fragrances in emulsions. A number of aroma chemicals were included in these studies—including phenylethyl alcohol, benzaldehyde, limonene and lavender oil. They demonstrated how fragrance partition is based on polarity and solubility, showcasing the systems’ change during evaporation. (For a summary of this work, see Bud Brewster’s account4 in the January 2006 issue of Cosmetics &Toiletries magazine.)

Beyond Three Variables

Once past three variables, the situation immediately turns ugly. For the curious, a generic quaternary phase diagram, drawn from metallurgy. These more complex diagrams don’t yield their secrets easily, but do show the incredible range of possibilities that arise by combining materials in different proportions.

Hot trends are always fun and exciting to ponder, but don’t ever forget the fundamentals. Phase diagrams provide powerful insight into personal care systems, telling us what happens when things are mixed together. Considering how chemists and formulators always are mixing things, it is hard to imagine cosmetic science without these marvelous triangles.